Stability Analysis of the Characteristic Polynomials whose Coefficients are Polynomials of Interval Parameters Using Monotonicity

Some Families of Graphs whose Domination Polynomials are Unimodal

Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=sum_{i=gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $gamma(G)$ is the domination number of $G$. In this paper we present some families of graphs whose domination polynomials are unimodal.

some families of graphs whose domination polynomials are unimodal

let $g$ be a simple graph of order $n$. the domination polynomial of $g$ is the polynomial $d(g, x)=sum_{i=gamma(g)}^{n} d(g,i) x^{i}$, where $d(g,i)$ is the number of dominating sets of $g$ of size $i$ and $gamma(g)$ is the domination number of $g$. in this paper we present some families of graphs whose domination polynomials are unimodal.

Analyzing the Stability Robustness of Interval Polynomials

Bounds on the coefficients of the characteristic and minimal polynomials

This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise inputdependant bounds on these coefficients. Such bounds are e.g. useful to perform deterministic chinese remaindering of the characteristic or minimal polynomi...

Stability of Polynomials with Time-Variant Coefficients

The problem of global asymptotic stability of a time-variant mth-order difference equation is addressed. Stable regions in the parameter space will be derived for two cases: the case of a time-invariant parameter region, and the case of a time-variant parameter region. These results find applications in the area of adaptive digital filters.